1. Field of the Invention
The present invention relates to multifocal optical devices such as multifocal ophthalmic devices, and methods for making such devices.
2. Description of the Related Art
A "phase zone plate" as the term is used in this document is an optical device utilizing a combination of a zone plate and one or more echelettes or steps in the zones. A phase zone plate typically includes concentric annular zones wherein the radii "r.sub.q " of the concentric annular zones are spaced substantially proportional to the square root of q, where q is an integer zone number. Specifically, the annular zones in a zone plate are spaced according to the following relationship: ##EQU1## where: .lambda.= the wavelength of light;
f = focal length of the positive or negative 1.sup.st order of diffraction; and PA1 q = zone number, an integer. PA1 d = depth of the echelettes; PA1 D.sub.0 = maximum depth of the echelettes; PA1 r = radial distance within the first two zones of the phase zone plate measured perpendicularly from the optical axis; and PA1 b = outside radius (r.sub.2) of the second annular zone. PA1 .lambda.= design wavelength; PA1 n = index of refraction of the lens material; and PA1 n'= index of refraction of the adjacent medium PA1 d = depth of the echelettes; PA1 D.sub.0 = maximum depth of the echelettes; PA1 r = radial distance from optical axis; and PA1 b = radius of first even zone (r.sub.2). PA1 .lambda.= design wavelength; PA1 n = index of refraction of the device or lens material; and PA1 n'= index of refraction of the adjacent medium. PA1 A(p) is a transmission profile of the device as a function of p; PA1 R is a first selected parameter; PA1 S is a second selected parameter; PA1 p is r.sup.2 /b.sup.2 ; PA1 r is a radial distance within a first and a second one of the zones of the multifocal phase zone plate measured perpendicularly from the optical axis; and PA1 b is an outside radius (r.sub.2) of the second annular zone.
Although the foregoing relationship establishes the focal length of a phase zone plate, by altering the step height of the echelettes within the zones, their refractive index, their surface profile, or any combination thereof, the relative distribution of light to the various orders of diffraction can be changed. "Phase profile" as used in this document refers to the optical phase shift profile resulting from the geometric surface profile of the phase zone plate surface and its refractive index through which light propagates as it enters or leaves the optical device.
The design of phase zone plates can be such that about 80 percent of the light incident on the phase zone plate, i.e., perpendicularly into the drawing sheet of FIG. 1, can be split and directed to the 0.sup.th and 1.sup.st orders, with about 40.5 percent being transmitted to each of those orders. The remainder of the light is transmitted to other spurious orders. For example, there is described in commonly owned copending application Ser. No. 456,226 (a continuation application of Ser. No. 280,899, now abandoned filed Dec. 7, 1988, which is a continuation-in-part of commonly owned application Ser. No. 863,069 filed May 14, 1986), now U.S. Pat. No. 5,017,000 a phase zone plate utilizing a geometric surface profile corresponding to a parabolic function, hereinafter called the parabolic surface profile. The parabolic surface profile is a repetitive profile with its basic pattern defined across the first two annular zones (bounded between r=0 and r=r.sub.2) as:
d =D.sub.0 (1-r.sup.2 /b.sup.2)
where:
The echelette or facet depth within the phase zone plate for an equal energy split between the 0.sup.th and 1.sup.st orders is given by: EQU D.sub.0 = 0.50 .lambda./(n -n')
where:
The associated phase profile is: EQU .phi.=.pi.(1 -r.sup.2 /b.sup.2)
and the intensity of light focused to the 0.sup.th and 1.sup.st orders is given by: EQU I.sub.0 =I.sub.1 =sinc.sup.2 (0.50)
where: EQU sinc(x) =sin(.pi.x)/(.pi.x).
In S.A. Klein and Zhuo-Yan Ho, "Multifocal Bifocal Contact Lens Design, " Proc. SPIE, Vol. 679, pp. 25-35, Aug. 1986, Table 2 and corresponding comments, it is confirmed that an optimum split of the transmitted light to two focal points, particularly at the 0.sup.th and the 1.sup.st orders, occurs for a phase zone plate having a parabolic surface profile in which the blazing has a maximum depth corresponding to one half of the design wavelength. According to Klein and Ho, the following intensities at the orders (m) are achieved for such a bifocal lens:
______________________________________ m Intensity ______________________________________ -4 .0050 -3 .0083 -2 .0162 -1 .0450 0 .4053 1 .4053 2 .0450 3 .0162 4 .0083 ______________________________________
Another example of altering the distribution of light intensities among various orders in a phase zone plate is provided in commonly-owned copending application Ser. No. 456,230 now U.S. Pat. No. 4,995,715 (a continuation application of Ser. No. 222,000, filed Jul. 20, 1988) now abandoned. The '230 application describes a phase zone plate having a surface profile corresponding to a cosine function, hereinafter called the cosine surface profile. The cosine surface profile is defined in terms of the following relationship: EQU d =D.sub.0 {1/2+1/2cos (.pi.r.sup.2 /b.sup.2)}
where:
The echelette or facet depth for an equal energy split between the 0.sup.th and 1.sup.st orders is given by: EQU D.sub.0 =0.405 .lambda./(n-n')
where:
The associated phase profile is: EQU .phi.=0.405 .pi.(1 +cos(.pi.r.sup.2 /b.sup.2))
and the intensity of light focused to the 0.sup.th and 1.sup.st orders is given by: EQU I.sub.0 =I.sub.1 =J.sub.0.sup.2 (0.405 .pi.) =0.403.
where: J.sub.0 =Bessel function.
Such a phase zone plate achieves an 81 percent transmission of the incident light to the 0.sup.th and 1.sup.st orders. The remaining 19 percent of the light is distributed among the spurious or subsidiary focal orders, also know as higher orders of diffraction.
It has now been determined that the distribution of incident light to the spurious or subsidiary focal orders significantly contributes to glare and haloing effects found in the use of ophthalmic lenses utilizing phase zone plates, especially those which maximize the transmission of light to the 0.sup.th and 1.sup.st orders. These effects have been found to cause discomfort to some wearers of ophthalmic lenses of such design, especially when the lenses are worn at night or in other low light conditions in the presence of a concentrated source of light, such as a distinctive light source surrounded by darkness or near darkness. Illustrative of such light sources are auto headlights and tail lights and street lamps. The causes of the glaring and haloing effects have been difficult to ascertain and only now are sufficiently understood that a solution to eliminate or ameliorate them is realizable.